Modified logarithmic Sobolev inequalities for canonical ensembles

Max Fathi (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this paper, we prove modified logarithmic Sobolev inequalities for canonical ensembles with superquadratic single-site potential. These inequalities were introduced by Bobkov and Ledoux, and are closely related to concentration of measure and transport-entropy inequalities. Our method is an adaptation of the iterated two-scale approach that was developed by Menz and Otto to prove the usual logarithmic Sobolev inequality in this context. As a consequence, we obtain convergence in Wasserstein distance $W_p$ for Kawasaki dynamics on the Ginzburg-Landau model.

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Physique mathématique [math-ph]

Max Fathi. Modified logarithmic Sobolev inequalities for canonical ensembles. ESAIM: Probability and Statistics, 2015, 19, pp.544-559. ⟨10.1051/ps/2015004⟩. ⟨hal-01874814⟩